B1 mapping in MRI system using k-space spatial frequency domain filtering

ABSTRACT

Frequency filtering of spatially modulated or “tagged” MRI data in the spatial frequency k-space domain with subsequent 2DFT to the spatial domain and pixel-by-pixel arithmetic calculations provide robust ratio values that can be subjected to inverse trigonometric functions to derive B1 maps for an MRI system.

BACKGROUND

1. Technical Field

This application describes methods and apparatus for generatingmulti-dimensional maps of the spatial distribution of radio frequency(RF) magnetic fields (typically labelled as the “B1” field) in MRI(magnetic resonance imaging) systems.

2. Related Art

Magnetic resonance imaging (MRI) systems are by now well known and manydifferent types of commercially available MRI systems are regularlyemployed for medical research and/or diagnostic purposes. Although thereare many variations in detailed image acquisition processes and/or MRIsystem geometries, they all share some basic fundamental principles.

For example, MRI systems all utilize the principle of nuclear magneticresonance (NMR) wherein nuclei having a net magnetic moment (e.g.,nuclei having an odd number of protons such as the hydrogen nucleus) areimmersed in a static background magnetic field B₀. Ideally, thisbackground static magnetic field is homogeneous throughout a volume tobe imaged (even in the presence of the intervening object to be imaged).This background magnetic field tends to align a significant number ofthe nuclei magnetic moments therewith so as to produce a rathersignificant net nuclei magnetization aligned with the homogeneousbackground magnetic field B₀.

The nuclear magnetic moments can be thought of as rotating about an axisat a frequency which is proportional to the magnetic field imposed uponthe nucleus at its particular spatial location. The so-called Larmorangular frequency ω=γβ where γ is a gyromagnetic ratio constant for agiven species of nuclei and its structural environment and β is thestrength of the imposed magnetic field. Accordingly, in an ideal world,a particular species of nuclei having common physical surroundings wouldall have a common Larmor frequency of rotation. However, bysuperimposing an auxiliary magnetic field having a linear gradient(e.g., in one of three orthogonal directions x, y, z), it will beappreciated that the Larmor frequency of such common species of nucleidisposed along the changing field gradient will now have differentvalues in accordance with the magnitude of the linear magnetic gradientfield at the spatial location of a given nucleus. Again, in an idealworld, such superimposed magnetic gradient field would have only anexactly linear gradient in one desired dimension and otherwise beuniform and homogeneous. Typically, an MRI system has three sets ofgradient coils arranged to impose linear magnetic gradient fields ineach of three different mutually orthogonal directions.

By transmitting an RF magnetic field at the Larmor frequency into thevolume that is to be imaged, one can selectively “excite” the nuclearmagnetic resonant (NMR) nuclei that happen to fall within a givenselected volume (e.g., a “slice”) so as to nutate the nuclear magneticmoment away from the nominal static magnetic field B₀. Depending uponthe amplitude and duration of such an exciting RF pulse, the magneticmoment of a nucleus can be “nutated” away from the nominal B₀ alignmentby controlled amounts (e.g., 90°). After such nutation, the nuclearmagnetic moment tends to relax back toward nominal alignment with B₀,but with characteristic longitudinal and transverse time constants T1,T2 and, in the process, each relaxing nuclear magnetic moment emits aradio frequency response signal that can be detected as an RF signalhaving a particular amplitude, frequency and phase (e.g., relative tothe exciting RF field and/or to other NMR nuclei emitting RF responsesignals).

By carefully choosing a particular “MRI sequence” of RF excitationpulse(s) and magnetic gradient pulses, one can elicit meaningfulspatially-encoded RF response signals so as to permit construction of animage or map of the NMR nuclei densities throughout a specific volume ofthe MRI system (e.g., a slice of the “imaging volume”). Over the lastseveral decades of MRI system development, a very large number of MRIsequences have been discovered and commercialized. Since most, if notall, such imaging sequences can be utilized in the following exemplaryembodiments, and since such are already well known to those skilled inthe art, further detail about specific MRI sequences is not required.

The RF excitation fields transmitted into the imaging volume as well asthe RF response fields received from the imaging volume are transmittedand/or received via RF coils which act as RF antennae. Once again, thereare many different RF coil geometries well known to those in the art.For example, there may be “head” coils, “surface” coils, “whole body”coils, “multi-coil arrays” and the like. All of these RF antennae/coilstructures serve to transduce electromagnetic radio frequency wavesto/from NMR nuclei in the imaging volume onto feed line(s) of the RFantennae/coils which are then connected appropriately to RF transmitterand/or receiver circuits (e.g., via a transmit/receive switch if thesame coil structure is used to both transmit and receive), as will beapparent to those skilled in the art.

Once again, in a perfect world, the RF antennae/coil sensitivitythroughout the volume to be imaged is desirably absolutely uniform andhomogeneous at all points within the volume to be imaged.

Unfortunately, the ideals of absolutely uniform homogeneity, absolutelylinear gradients, etc., desired for various magnetic/RF fields in theMRI system are not realized in practice. Accordingly, various “shimming”attempts are made to correct for unwanted departures from the idealand/or to compensate acquired signals that have been adversely affectedby such less than ideal circumstances.

This application is directed towards a new and improved technique formapping of the RF B1 magnetic field associated with transmit sensitivityof the RF antennae/coils of an MRI system. Various prior techniques havebeen used for generating such B1 maps which are then used either toimprove the design of the MRI system itself and/or to providecompensated output images from the MRI system (e.g., especially wherequantitative measurements are to be made based upon such images).However, as will be explain below, such prior techniques leave room forimprovement—which the exemplary embodiments explained in detail belowprovide.

Some examples of prior approaches that may be relevant to the presentapplication are identified below:

-   -   1. L. Axel, L. Dougherty, “MR Imaging of Motion with Spatial        Modulation of Magnetization,” Radiology, Vol. 171, pages 841-845        (1989)    -   2. L. Axel, L. Dougherty, “Heart Wall Motion: Improved Method of        Spatial Modulation of Magnetization for MR Imaging,” Radiology,        Vol. 172, pages 349-350 (1989)    -   3. E. K. Insko, L. Bolinger, “Mapping of the Radiofrequency        Field,” J Magn Reson (A), Vol. 103, pages 82-85 (1993)    -   4. R. Stollberger, P. Wachs, “Imaging of the Active B₁ Field in        Vivo,” Magn Reson Med, Vol. 35, pages 246-251 (1996)    -   5. N. G. Dowell, P. S. Tofts, “Fast, Accurate, and Precise        Mapping of the RF Field In Vivo Using the 180° Signal Null,”        Magn Reson Med, Vol. 58, pages 622-630 (2007)    -   6. F. Jiru, U. Klose, “Fast 3D Radiofrequency Field Mapping        Using Echo-Planar Imaging,” Magn Reson Med, Vol. 56, pages        1375-1379 (2006)    -   7. J. T. Vaughan, M. Garwood, C. M. Collins, W. Liu, L.        DelBarre, G.

Adriany, P. Anderson, H. Merkle, R. Goebel, M. B. Smith, K. Ugurbil, “7Tvs. 4T: RF Power, Homogeneity, and Signal-to-Noise Comparison in HeadImages,” Magn Reson Med, Vol. 46, pages 24-30 (2001)

-   -   8. J. Wang, W. Mao, M. Qiu, M. B. Smith, R. T. Constable,        “Factors Influencing Flip Angle Mapping in MRI: RF Pulse Shape,        Slice Select Gradients, Off-Resonance Excitation, and B₀        Inhomogeneities,” Magn Reson Med, Vol. 56, pages 463-468 (2006)    -   9. V. L. Yarnykh, “Actual Flip Angle Imaging in the Pulses        Steady State: A Method for Rapid Three-Dimensional Mapping of        the Radiofrequency Field,” Magn Reson Med, Vol. 57, pages        192-200 (2007)    -   10. M. A. Bernstein, K. F. King, X. J. Zhou, Handbook of MRI        Pulse Sequences, Elsevier Academic Press, especially pages        166-171 (2004)    -   11. X. Chen, X. Shou, W. R. Dannels, “Feasibility of Rapid B1        Mapping with RF Prepulse Tagging,” Proceedings of ISMRM, 16^(th)        Scientific Meeting, Toronto, Canada, May 2008 Abstract #3045    -   12. X. Chen, X. Shou, W. R. Dannels, “Feasibility of Rapid B1        Mapping with RF Prepulse Tagging,” poster presented at Research        Showcase 2008, Case Western Reserve University, Veale        Convocation Center, Cleveland, Ohio, Apr. 16-17, 2008.

MRI requires both transmitted radio frequency (RF) fields and receivedradio frequency (RF) fields. These RF fields are often denoted as B1fields. The transmitted field, in typical usages, should beapproximately uniform over the area being imaged within the subject.Spatial inhomogeneities of the RF fields introduce unwanted effects,including various artifacts in images, degradations in image contrast,or degradation or failure of various quantification methods. Thetransmit field acting within human bodies exhibits greaternon-uniformity as main magnet field strength increases. The staticmagnetic main field is denoted as the B₀ field. The effective B1 fieldsdepend both upon the engineering design of the MRI scanner (such as RFantenna/coil geometry), and the geometry and electromagnetic propertiesof the subject within the scanner (often a human patient).

Having information about the distribution of non-homogeneity in thetransmit B1 field within a specific subject can be beneficial in variousways. Advantages of having such data include being able to betterinterpret images and artifacts, being able to spatially improve theactual field patterns by improved design of the scanner, being able tointeractively or dynamically refine the fields on specific subjects andin specific scan areas, and being able to improve or correct theacquired data and/or resulting images. In some more advanced methods,such as “multichannel transmit” or “Transmit SENSE,” knowledge ofnon-uniform spatial field patterns is explicitly needed and explicitlyused to accomplish goals of improved RF excitation and spatiallocalization.

Numerous methods exist or have been proposed for experimentallydetermining the B1 field. When the information is determined orpresented in the form of a 2-D or 3-D spatial distribution, it is calleda B1 map.

A pulse sequence can be repeated several times using successiveamplitudes of RF excitation (i.e., nutation) pulses. The receive MRsignal intensity is known to have a certain functional dependence on theeffective B1 transmit amplitude, such as:

S(θ(x,y,z), x,y,z)=[ρ(x,y,z)]*sin(θ(x,y,z))³   [Equation 1]

θ(x,y,z)=RF_ampl_factor*(B1_spatial(x,y,z))   [Equation 2]

where:

-   -   S is measured data (using a pulse sequence acquisition at the        scanner for various RF_ampl_factor values), and the unknown        value of B1_spatial (i.e., θ or B1_spatial) are the spatial        distribution(s) to be determined;    -   “S” denotes the MR signal intensity (the actual mathematical        functional dependence is based upon the pulse sequence used);    -   ρ is a signal strength factor such as the proton density, or a        proton density times the receive coil sensitivity, or the like;    -   RF_ampl_factor is an independently adjusted control factor        (e.g., RF pulse amplitude and duration) in the pulse sequence;    -   B1_spatial(x,y,z) is the form of a spatially dependent B1        associated with some reference value of the RF_ampl_factor; and    -   θ has the meaning of the spatially dependent effective B1 field.

The specific “S” formulae given above happen to be suitable for a pulsesequence producing a single stimulated echo with complete T1/TR signalrecovery, and minimal T1, T2 decay during the echo time, just as anexample.

In general, one detects or measures S, from which one can determine θ,from which one can determine B1_spatial. In the literature, sometimesauthors compute and report θ, and sometimes they compute and report B1.Converting from one to the other is simple, and the two terms may beused somewhat interchangeably throughout the following description.

To be rigorous, B1_spatial should represent an instantaneous physicalmeasurement of a component of a time-varying magnetic field. θ is thetime integral of (γB1), and γ is a gyromagnetic ratio. The time integralcan be a simple linear approximation or, more accurately, it can be theresult of integrating out the full Bloch equations. These relationshipsare well known in MRI, and are not discussed further here. Suffice it tosay, conversion between B1 and θ is straight-forward under typicalimaging conditions.

Multiple measurements are generally needed, so that from multiple valuesof S, it is possible to solve for “ρ” and θ.

Spatially localized images can be collected at a series of amplitudes.Analysis such as searching for a peak, or fitting a curve, can be doneto determine the strength of B1. In a simple exemplary case, such as astimulated echo sequence where S=S(θ)=sin(θ)³, if we assume anapproximately uniform B1_spatial(x,y,z), MR data can be collected ateach of several RF_ampl_factor values over some nominal range. TheRF_ampl_factor which yields the peak of the signal value “S” correspondsto θ(x,y,z)=π/2 (flip angle in radians), i.e., at the particularRF_ampl_factor for which S achieves a maximum,B1_spatial=(π/2)/RF_ampl_factor (once again, ignoring other factors suchas γ, the RF pulse duration, etc.).

Other pulse sequences can be used, and other features of the signalstrength function can be used, such as the first minimum of the signalfor a 180° excitation pulse sequence, or such as themost-negative-valued signal for a 180° inversion pulse followed by asign-sensitive readout.

The successive amplitudes can be controlled by stepping through a rangein a prescribed fashion, perhaps linear increments across some nominalrange, or by iterative search methods like bisection, etc.

The varying amplitude factor, RF_ampl_factor, can be altered and appliedto all RF transmit pulses in a sequence in unison or, alternately, oneor a few pulses can be modified, while others are kept constant. Forexample, in a spin echo pulse sequence with two nutation pulses (α1 andα2), the signal strength can have the form:

S(α1, α2)=sin(α1)*(sin(0.50 α2))²,

in which case α1 and α2 may be varied together, or either one can bevaried independently.

When B1_spatial(x,y,z) is not treated as constant (i.e., spatiallyhomogeneous), a simple but slow technique is to acquire and generateentire 2-D or 3-D images for each of several RF gain factors, and thento analyze the sets of images pixel-by-pixel, to fit or search for anamplitude scaling at each pixel location. Note that while using searchalgorithms and data-dependent choice of RF_ampl_factor to try toconverge to some optimal condition may be a good strategy when B1 isspatially uniform, it is not as suitable when B1 is non-uniform. A valueof RF_ampl_factor which achieves a goal such as a signal null at onelocation will not simultaneously achieve nulls at other locations, forexample.

The resulting B1 strengths, or flip angles θ, are then collected andpresented or stored in the form of an image, known as a B1 map. It ispossible that the B1 value can be treated either as a magnitude or as acomplex value which also includes some phase value (relative to asuitable or arbitrary reference phase).

Many acquisition methods are known which can be used to determine B1.Basically, all MRI pulse sequences have dependencies on B1 transmitfields, but some have more favorable characteristics, such as nearlylinear dependencies over a range of transmit values, or such asdependencies which are uncoupled from other variables like the tissue T1and T2 parameters. Corresponding analysis methods also exist, often forspecific acquisition methods.

In some cases, a series of many RF pulse amplitudes are used insuccessive acquisitions. A feature such as a null or minimum in thesignal level can then indicate which RF pulse amplitude is the nearestmatch to a certain flip angle or a certain B1 strength, as previouslyexplained.

Determining θ from S may be done in any of a few ways. There can be someregression or fitting to yield both ρ and S (even though there may be noexplicit interest in ρ). There could be a simple search for a simplefeature of the signal curve such as a maximum or null. There are ways tocollect a few values of S, (perhaps something like S1 usingRF_ampl_factor=RF_amp_factor1, and S2 usingRF_ampl_factor=(2*RF_ampl_factor1), then finding a closed formmathematical dependence of θ on S1 and S2, especially where thatclosed-form dependence has eliminated other variables like ρ.

It is common to collect pairs of images acquired with different numbersof RF pulses, or different amplitudes, and then form ratios of theimages. The ratios cancel other factors contributing to image intensity,leaving terms which depend on the RF pulses. The signal ratios havedependencies upon the RF pulse amplitudes which can be computed andinverted.

We have previously described collecting data with a few values ofRF_ampl_factor, each using the same pulse sequence and the sameacquisition parameters (other than RF_ampl_factor). A variant of thisidea, is to acquire instead two (or more) pulse sequences, two or moreechoes, or the like. In one example, the two basic pulse sequences couldbe different, and each has a different functional dependence of S on θ(e.g., one spin echo with a saturation or inversion pre-pulse, and asecond spin echo without the pre-pulse). In another example, two or moreechoes can be acquired in a single, more complicated, pulse sequence(e.g., a spin echo and a stimulated echo, or some kind of first RF echoand second RF echo). In yet another example, a pulse sequence can be runwith two sets of parameters, such as a short TR and a long TR, perhapsin an interleaved fashion.

One commonly referenced method which is an example of such a ratiocalculation is the double angle method. (Insko, 1993; Stollberger, 1996,etc.)

It is known that RF tagging techniques (including “SPAMM”) depend uponRF amplitudes, and so they can be used for determining B1 spatialdependencies (B1 maps). (Axel, 1989, two references.)

In SPAMM RF tagging, two or more similar RF tagging nutation pulses areapplied, and a pulsed gradient is applied in between them. The gradientcauses spatial “modulation patterns.” One simple pattern is a periodicset of parallel stripes, with each cycle showing a generally sinusoidalintensity pattern. A simple physical explanation is that the two RFpulses can have similar effects individually, but the gradient appliedafter the first pulse causes a spatially dependent phase factorassociated with the first RF tagging pulse. Then, depending upon thisphase factor, the two RF tagging pulses may “add constructively” or“cancel each other like a destructive interference.” Thus, a series ofstripes is generated, with bright untagged signal appearing at locationswhere the tagging pulses cancel each other, and with tagged reduced(dark) signal bands appearing in locations where the effects of the twoRF tagging pulses combine together constructively. A mathematicaldescription of this is given in Bernstein, King and Zhao, pages 166-171,2004.

Bernstein at page 176 has a cursory reference to the fact that SPAMMpre-pulses can be used to figure out B1 maps. There are also somesimilar cursory references in one or both of the original Axel papers.While such references say it can be done, the inventors are not aware ofanyone really doing it or publishing results until they did a version atthe ISMRM Toronto May 2008 conference—and that was with purelyimage-based processing. When considering prior art use of SPAMM toachieve B1 mapping, it appears that there is limited published material.

The Axel papers allude to the fact that spatial tagging lines may appearas pairs of minima under certain conditions, and that the spatialseparation of the pair of minima could be used to determine B1. Theconditions for favorable application of this acquisition method andanalysis approach can include a total tagging excitation higher than 90°(perhaps between 110° and 270°), magnitude image reconstruction, andimage pixel resolution of multiple pixels across each full spatial cycleof the complicated tagging pattern.

Suppose the two pulses each have some nominal amplitude at a particularlocation, each yielding (perhaps) 35° tip angle in some region. Thetagging portion of the acquisition sequence can then be described ashaving a total tagging RF nutation angle of 70°, which dictates thepercentage of signal suppression at a trough in that region.

The prior Dannels, Chen and Shou approach using SPAMM-tagging for theacquisition (but a different analysis concept from that now to bedescribed below) prefers a different set of favorable acquisitionconditions. When the total tagging RF angle is less than about 90°, thenthe relative darkness of tagged areas can be used directly to determinethe tagging RF angle. The resultant image has a structure of alternatingbands or stripes, with both tagged and untagged signal. Bright peaks areuntagged, and the darkest part of each trough corresponds to a locationwhich is affected by the total tagging RF pulse's total B1 angle. Undersuch conditions, the ratio of a peak to a trough can then be sufficientto determine the effective B1 field. With such a strategy, the peak andtrough are acquired totally simultaneously, in a single image. Thus,there should be minimal concerns about the sources of inconsistencieswhich exist between two or more measurements. (Patient motion is themost notorious source of these inconsistencies.) This is an intrinsicadvantage of using the tagged image. In exchange for getting away fromthe data-consistency problem of using two or more acquisitions, thetagging method will, however, depend upon other consistency concernsacross two or more locations. For example, the signal strength ratio isattributed to an RF tagging pulse (difference between a peak and atrough) and its local B1 field, so there should not be other majorsources of deviation in “S”, such as confounding differences due to “ρ”or T1 or T2.

In an abstract submitted in November 2007 to the ISMRM conference of May2008, one of the inventors (plus co-authors Chen and Shou) presentedanalysis of a method of detecting nearby peaks and valleys in an imagewith tagging, to compute the effective RF pulse amplitude which createdthe tag. The inventors consider this to be not a particularly effectivemethod. (See “Feasibility of Rapid B1 Mapping with RF Prepulse Tagging,”X. Chen, X. Shou, W. Dannels, Proceedings of ISMRM 16^(th) ScientificMeeting, Toronto, Canada, May 2008 abstract #3045.) Also documentingthis approach is a poster which analyzes use of the same taggingacquisition, but using the (image-domain) processing of peaks andvalleys. This poster was presented at Case Western Reserve University inApril 2008.

Many of such prior techniques for B1 mapping have limitations ofacquisition speed. For example, one minute for a 2-D map, or fourminutes for a 3-D volume map, have been touted as being “fast” B1mapping techniques. Motion artifacts in the body can degrade individualimages, but more importantly, they can cause inconsistencies betweenpairs of images. Inaccuracies and biases can arise. Effects from T1decay have been often analyzed. Techniques may require additionalcorrections or calibration (e.g., double angle is known to have aconfounding effect, where selective excitation slice thickness andprofiles exhibit an undesired dependence upon the local B1). (See Wang,2006.) Arrival of signal level to equilibrium or steady state values canbe slow, e.g., on the order of a few times T1. This can limit scan timeor limit temporal resolution, or introduce errors in the presence ofattempted faster acquisitions. Intrinsic SNR can adversely affectaccuracy, resolution or scan acquisition time. There can be a limiteddynamic range with respect to the deviation of B1 relative to a knownnominal value. (See, for example, Dowell, 2007.) The associatedacquisition technique for reading out the image may have limitations orartifacts, which would propagate into the associated maps. For example,EPI, as used in Jiru, 2006, can have significant geometric distortion,or chemical shift, or utilizes fat suppression, making it impractical todetermine the B1 within fat.

Most of the prior techniques require longer acquisitions, costingseveral minutes of scanning for 2-D or 3-D maps. In many of thesetechniques, the different acquired images depend on not only RF pulseamplitudes, but also other factors such as T1, T2, or resonancefrequency shifts, etc. This becomes a source of error in the resultingB1 determination, or else requires additional acquisitions tosimultaneously determine both B1 and the other factors. When scans arelonger, or more than one scan must be combined, physiological motion candegrade the individual acquired images, or make the separate imagesbecome inconsistent, ruining the ratios. Motion artifact can maketechniques useless in human torsos. Using single tagged images avoidsthese problems, but requires more sophisticated processing. Detection oflocal signal variations in a tagged image, when the unmodulated imageitself contains significant local variation, is not easy, especiallywhen working in the image domain.

If the SPAMM acquisition is used with image-domain peak-and troughdetection method, significant error can arise if a neighboring peak andtrough are used together in a ratio, but they have other confoundingeffects, like major differences in ρ.

BRIEF SUMMARY

This application describes an improved way to determine spatial patternsand amplitudes of transmit RF fields in MRI systems. When used inconjunction with suitable MRI acquisition pulse sequences, measurementsof patterns are produced which will depend both upon the design of thescanner and upon the subject. Thus, experimental measurement anddetermination on individual patients is more suitable than, say,theoretical calculations for a single patient or single geometric model.The technique can be especially advantageous at higher field strengths,in bodies and abdomens, or in cases where acquisition speed isimportant, or where motion in the body can make measurement problematic.

The current application describes a method for determining orcalculating B1 maps, from experimentally acquired MR data of a suitablekind. In particular, advantages can be realized in accuracy or practicalperformance or speed when generating B1 maps, especially inside humansor moving, living subjects.

Sometimes transmit fields are denoted by Tx, or Tx B1, or the like, andbecause they can exhibit a certain polarity of circular polarization,they can also be denoted as B1⁺. Similarly, receive RF fields associatedwith samples and coils can be denoted as Rx, or Rx B1, or B1⁻, etc.

The exemplary embodiments to be described below generate a B1 map of RFB1 signal magnitude values in a MRI system by using an MRI system to:

-   -   acquire at least one two-dimensional set of B1 amplitude-tagged        MRI data signals in spatial frequency domain k-space from MR        nuclei within an imaged volume of the MRI system;    -   process such k-space data to produce at least two of three        sub-sets of frequency-filtered k-space data (e.g., a baseline        low frequency sub-set, and at least one of (a) a higher        positive-frequency sub-set and (b) a higher negative-frequency        sub-set, such higher frequency sub-sets including respectively        corresponding harmonic versions of the baseline sub-set);    -   separately transforming each of these at least two filtered        sub-sets to respectively corresponding spatial domain data sets        (e.g., a baseline magnitude set, and at least one of (a) a        positive harmonic magnitude set and (b) a negative harmonic        magnitude set);    -   arithmetically combining the baseline magnitude set with the        harmonic magnitude sets on a pixel-by-pixel basis to provide        upper and lower magnitude envelope data sets;    -   processing the upper and lower magnitude envelope data set        values on a pixel-by-pixel basis to generate a B1 map data value        based on an inverse function (e.g., trigonometric in the        exemplary embodiments where sinusoidal tagging is used) of a        value related to a ratio of the upper and lower pixel data        values at a given pixel location in the spatial domain; and    -   storing or displaying the B1 map data values for use in MRI        system design and/or correcting/compensating diagnostic MR        images taken by the MRI system (e.g., perhaps on a        patient-by-patient basis).

Preferably, the acquisition of k-space data from MR nuclei is achievedby applying at least two RF excitation pulses with at least oneinterleaved magnetic gradient pulse in a pre-sequence before applying anMRI pulse sequence (e.g., one of the many conventional well known MRIpulse sequences) to elicit successive MR responses in the time domainwhich are then mapped to respectively corresponding positions of k-space(e.g., typically to provide successive, respectively corresponding,lines of a multi-dimensional set of k-space data in a spatial frequencydomain.)

There are also advantages to be had if the original k-space data set is(a) two-dimensionally Fourier transformed to the spatial domain, and (b)further two-dimensionally Fourier transformed back to the spatialfrequency domain k-space before further processing. This detour to thespatial domain and back again to k-space has been discovered to provideadvantages in that it may produce a more idealized k-space data set forB1 mapping purposes. For example, if the MRI system happens to usemultiple receiver coils with outputs that are combined to achievecomplete data acquisition and/or uses parallel imaging techniques and/oruses complex-conjugate filling of a part of a k-space, etc., thenexperience has shown that a more idealized “starting” k-space data set(for B1 mapping) results from detouring into the spatial domain and backagain into the spatial frequency domain.

The spatial-tagging pre-pulse sequence may also be of many differenttypes. For example, there are well known tagging sequences such as theSPAMM (spatial modulation of magnetization) sequence and/or the DANTE(delays alternating with nutation for tailored excitation) sequence.Such tagging sequences can produce sinusoidally varying spatialmodulation which permits trigonometric inverse functions to be used asin the exemplary embodiments. Other tagging sequences may producenon-sinusoidal modulation, thus necessitating use of alternate inversefunctions.

The acquisition of a “starting” k-space data set may also involvemultiple data acquisition cycles and combining of the resulting k-spacedata. For example, it has been found particularly suitable to acquire afirst set of k-space data using a first tagging pre-sequence of at leasttwo RF excitation pulses having the same sense of nutation angle andthen also acquiring a second set of k-space data using a second taggingsequence of at least two RF excitation pulses having different,alternating nutation angle senses. The two sets of thus acquired k-spacedata are then arithmetically combined to produce a combined set ofk-space data to be used as a “starting” k-space data set in subsequentsteps of an exemplary embodiment. As will be explained in more detailbelow, this multiple acquisition and combination of k-space data canitself result in favorable reduction of harmonic content for the“starting” k-space data set to be used thereafter in an exemplary B1mapping process.

Once a suitable “starting” k-space data set has been acquired (which maybe a single first-acquisition k-space data set without detours orfurther preliminary processing), then it is spatial frequency-filteredin k-space by extracting k-space data from different portions of thek-space spatial frequency data set. In particular, the baseline lowfrequency sub-set of k-space is extracted, as well as at least onehigher frequency harmonic-containing portion of k-space data (e.g.,extracted from two other adjoining areas of k-space such as a strip ofk-space located above the baseline strip and a strip of data locatedbelow the baseline in k-space). The extraction may be made with respectto strips or rectangular/square (or other shaped) windows in k-space(possibly having sharp or weight-shaped edges) so as to, in effect,perform a frequency-filtering function since the k-space data is alreadyin the spatial frequency domain.

The frequency-filtered k-space extract data is then two-dimensionallyFourier transformed so as to bring it to the spatial domain—thusproviding at least two sets of spatial domain data—where by using onlymagnitude values for each data point, one can effectively de-modulatethe harmonic higher frequency data and be left with “envelope”-definingsets of values—one representing a low-frequency component and onerepresenting higher frequency, demodulated components (e.g., locatedabove (and/or below) the baseline component in k-space).

If the magnitude values from all sets of resulting spatial domain dataare added on a pixel-by-pixel basis, this provides a map of the peak or“upper” signal magnitude envelope. Similarly, subtracting from thebaseline magnitude set, on a pixel-by-pixel basis, the harmonicmagnitude set(s) provides a map of trough or “lower” signal magnitudeenvelope values.

Once such minimum and maximum pixel values have been determined, then a“tag depth” ratio data set may be created on a pixel-by-pixel basiswhere, for example, each pixel of tag depth ratio data TD=min/max wheremin is the lower magnitude data set value and max is the upper magnitudedata set value. One may then calculate the arccos of the tag depth ratiovalues (cos⁻¹ TD) on a pixel-by-pixel basis so as to provide a B1 map ofeffective tag nutation flip angles θ. Of course, once the effectivenutation flip angles θ are known, then the corresponding B1 magneticfield strengths may be calculated based on known formulae to provide aB1 map of effective B1 magnetic field strengths. Either the B1 map ofeffective nutation flip angles θ or the B1 map of effective fieldstrengths B1 may, of course, be normalized by ratioing such values withthe nominal desired value of θ or B1 provide a map of normalized B1field strengths and/or flip angles θ.

Any of these types of B1 maps may, of course, be displayed on a screenor printer for visual observation/use (e.g., in designing MRI systemchanges and/or quantifying MRI images, “correcting” or “compensating”such MRI images, etc.).

Some advantages of this exemplary embodiment are:

-   -   Compared to image-domain detection of peaks and troughs with        tagged data, the exemplary processes reduce or remove errors        from unequal baseline signals being used within a single ratio,        and in a single determination of B1 in a region.    -   The exemplary processes remove the need to locally fit to        determine the actual height of a peak, (or the actual minima of        a trough) when the location of the peak (or trough) is not        centered on a pixel. If uncorrected, this would normally lead to        underestimation of the signal level difference between peaks and        troughs and, therefore, would lead to a bias towards        underestimating the B1 level and the flip angle θ.    -   The exemplary processes remove the bias which could arise when        there is partial averaging of the tagging waveform within a        pixel of finite extent.    -   The exemplary processes are amenable to true single-shot        readout, as a way to get rid of inconsistencies from human        motion (e.g., temporal resolution of much less than 100 msecs        can be obtained).    -   The exemplary processes can be easily used in a breathhold, to        gain immunity against respiratory motion artifacts.    -   Since the main acquisition method can be changed to use various        pulse sequences, there can be a wide range of resolution and        sensitivity to MRI parameters, i.e., it is possible to choose a        sequence with higher spatial resolution, or better sensitivity,        or reduced sensitivity to motion.    -   The exemplary processes can be used in the presence of diverse        tissue types, including fat.    -   The exemplary processes can be fully automated, and do not        require secondary inputs such as T1 maps, or off resonance maps,        or estimates of T2 or T2*.    -   The exemplary processes have high dynamic range, even without        extending the usable signal analysis range beyond 90° total        tagging angle. For example, one acquisition can capture a range        of flip angles from 20° to 80°, i.e., a dynamic range of 4-to-1.    -   The exemplary processes have high immunity to noisy images, as a        result of good filtering.    -   The exemplary processes have the ability to get good spatial        resolution, if desired (maps of 32×32 or less are not unusual        with some other methods).    -   The exemplary processes allow higher resolution, in terms of tag        lines being potentially closer together, than in        image-domain-based analysis of the tag lines. Note that the        filtering step, or the step of generating an envelope of the        modulation part, will generally introduce a blurring or loss of        resolution in the B1 map, which is on the order of the spacing        of the tag lines. Thus, closer tag line spacing, such as two,        three or four pixels per cycle, as opposed to, say, 5-10 pixels        per cycle, can yield a higher resolution B1 map.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and advantages of the exemplary embodiments willbe apparent from the following more detailed description taken inconjunction with the accompanying drawings, in which:

FIG. 1 is a general overall schematic depiction of an MRI systemconfigured to practice the exemplary embodiments;

FIG. 2 is a schematic depiction of a pre-sequence to be employed inconjunction with a following MR imaging sequence so as to acquirespatially-tagged k-space data for use in the exemplary embodiments;

FIG. 3 is a schematic diagram, at a relatively high level, of exemplaryprocesses utilized in the exemplary embodiments for B1 mapping in an MRIsystem using k-space spatial frequency domain filtering;

FIG. 4 is a more detailed schematic flowchart of process control programcode structure that may be utilized in an exemplary embodiment of theMRI system shown in FIG. 1;

FIG. 5 is a schematic diagram of k-space filtering utilized in analternative embodiment;

FIG. 6 is also a schematic diagram of k-space frequency filteringutilized in an alternate embodiment;

FIG. 7 is a schematic diagram of an embodiment utilizing first andsecond data acquisition cycles with different tagging pre-pulsesequences followed by combination of the resulting k-space data sets soas to produce an improved “starting” k-space data set;

FIG. 8 is an image of a human pelvis with visible spatial modulationtagging lines superimposed thereon from use of a pre-pulse taggingsequence;

FIG. 9 is a B1 map generated from the tagged image of FIG. 8; and

FIG. 10 is a normalized B1 map from FIG. 9 with superimposed contourlines depicting variations in B1 effective magnitude across the humanpelvis.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

The MRI system shown in FIG. 1 includes a gantry 10 (shown in schematiccross-section) and various related system components 20 interfacedtherewith. At least the gantry 10 is typically located in a shieldedroom. One MRI system geometry depicted in FIG. 1 includes asubstantially coaxial cylindrical arrangement of the static field B₀magnet 12, a G_(x), G_(y) and G_(z) gradient coil set 14 and an RF coilassembly 16. Along the horizontal axis of this cylindrical array ofelements is an imaging volume 18 shown as substantially encompassing thehead of a patient 9 supported by a patient table 11.

An MRI system controller 22 has input/output ports connected to display24, keyboard 26 and printer 28. As will be appreciated, the display 24may be of the touch-screen variety so that it provides control inputs aswell.

The MRI system controller 22 interfaces with MRI sequence controller 30which, in turn, controls the G_(x), G_(y) and G_(z) gradient coildrivers 32, as well as the RF transmitter 34 and the transmit/receiveswitch 36 (if the same RF coil is used for both transmission andreception). The MRI sequence controller 30 includes suitable programcode structure 38 for implementing a spatial-modulation pre-sequence(e.g., SPAMM or DANTE) in conjunction with other (e.g., conventional)MRI sequences already available in the repertoire of the MRI sequencecontroller 30.

The MRI system 20 includes an RF receiver 40 providing input to dataprocessor 42 so as to create processed image data to display 24. The MRIdata processor 42 is also configured for access to a B1 map program codestructure 44 and to a B1 map memory 46 (e.g., for storing B1 map dataderived from processing in accordance with the exemplary embodiments andthe B1 map program code structure 44).

Also illustrated in FIG. 1 is a generalized depiction of an MRI systemprogram store 50 where stored program code structures (e.g., for B1mapping based on spatial frequency domain analysis) are stored incomputer-readable storage media accessible to the various dataprocessing components of the MRI system. As those in the art willappreciate, the program store 50 may be segmented and directlyconnected, at least in part, to different ones of the system 20processing computers having most immediate need for such stored programcode structures in their normal operation (i.e., rather than beingcommonly stored and connected directly to the MRI system controller 22).

Indeed, as those in the art will appreciate, the FIG. 1 depiction is avery high level simplified diagram of a typical MRI system with somemodifications so as to practice exemplary embodiments to be describedhereinbelow. The system components can be divided into different logicalcollections of “boxes” and typically comprise numerous digital signalprocessors (DSP), microprocessors, special purpose processing circuits(e.g., for fast A/D conversions, fast Fourier transforming, arrayprocessing, etc.). Each of those processors is typically a clocked“state machine” wherein the physical data processing circuits progressfrom one physical state to another upon the occurrence of each clockcycle (or predetermined number of clock cycles).

Not only does the physical state of processing circuits (e.g., CPUs,registers, buffers, arithmetic units, etc.) progressively change fromone clock cycle to another during the course of operation, the physicalstate of associated data storage media (e.g., bit storage sites inmagnetic storage media) is transformed from one state to another duringoperation of such a system. For example, at the conclusion of a B1mapping process, an array of computer-readable accessible data valuestorage sites in physical storage media will be transformed from someprior state (e.g., all uniform “zero” values or all “one” values) to anew state wherein the physical states at the physical sites of such anarray vary between minimum and maximum values to represent real worldphysical events and conditions (e.g., the sensitivity map for an RFantenna/coil over an imaging volume space). As those in the art willappreciate, such arrays of stored data values represent and alsoconstitute a physical structure—as does a particular structure ofcomputer control program codes which, when sequentially loaded intoinstruction registers and executed by one or more CPUs of the MRI system20, cause a particular sequence of operational states to occur and betransitioned through within the MRI system.

The exemplary embodiments described below are superior ways to processacquisitions and compute B1 maps from images which have intensitymodulation from tagging pulses.

The acquired single image has a spatial modulation imposed on it. Thespatial frequency of the modulation is known. The amplitude of themodulation depends upon the strength of RF pulses and hence the spatialB1 (transmit field) dependency. Raw MR data (k-space data) for thesescans includes a central section which generates the unmodulated (i.e.,low-frequency base band) part of the image.

In a preferred embodiment, the k-space data is reconstructed to an imagein the spatial domain in the usual way, including an (inverse) 2DFT andtaking magnitude of the complex image. A further (forward) 2DFT is thenused to convert it back to the k-space spatial frequency domain whichcontains shifted replicas which generate the higher frequency modulatedcomponents of the image. Simple windowing operations separate themodulated and unmodulated components (in k-space). The k-space dataincludes a “low-pass” unmodulated part of the signal, a “high-pass”modulated part with a positive spatial frequency, and a “high-pass”modulated part with a negative spatial frequency. Each of the parts (thetwo modulated parts and the unmodulated part) are then independentlytransformed back to the image domain. Taking magnitude (in the imagedomain) of complex quantities demodulates the modulated parts. One mightchoose to call these contributions “modulated-unmodulated” parts. Sumsand differences of those parts, in turn, give robust maps of the maximalsignal envelope and minimal signal envelope. The unmodulated part plusthe modulated-unmodulated parts gives the peak envelope. The unmodulatedpart, minus the modulated-unmodulated parts gives the trough envelope.These generated envelopes are more accurate than quantifying peaks andvalleys in the image domain. The technique is fast enough to beacceptable for calibrations or pre-scans, if needed, in clinicalscanning applications.

The filtering in k-space can be done by multiplying the data by, forexample, two, three (or more) window functions. A first window, for thelow pass, can be positioned over the center of k-space, i.e., the D.C.component. Alternately, it is feasible to search the k-space data todetect the location with the highest peak, and to use that as the centerfor the low-pass window.

The locations at which to apply the at least one high-pass window (e.g.,two in this exemplary embodiment, one for positive and one for negativespatial frequencies, respectively) can be determined in any of a fewways. The area of the gradient pulse used between the two RF taggingpulses can be multiplied by a Larmor frequency, to give a k-spacedistance, in units such as cycles per centimeter. This distance, plusknowledge of the imaging field of view, can be used to determine adistance in terms of a number of samples (presuming for example,critical Nyquist sampling rates). As an example, if the gradient arearesulted in a cycle of accumulated phase every 6 millimeters, and if theimaging field-of-view were 24 centimeters, then the modulation amountsto 40 cycles of modulation across the image. Thus, by the Fourier shiftprinciple, the modulated parts will be displaced by 40 samples to eitherside of the unmodulated low-pass central data. Therefore, one maymultiply one copy of the k-space data by a window shifted 40 indices toone direction, and multiply another copy of the k-space data by anidentical window shape, but displaced 40 indices in the oppositedirection from the center. The particular window functions any of a wideset of shapes, such as Hanning, Hamming, Gaussian, Kaiser-Blackman,Fermi functions, etc., as are well known in signal processing and inMRI. An alternative to calculating the shift from gradient and sequenceparameters is to search the k-space data to detect the location of thesesecondary peaks.

The windowing operations in k-space provide a kind of filtering andreduce noise, allowing better determination of peak and trough signal.But a more significant advantage arises from the fact that theunmodulated-modulated image-domain data and the low-pass unmodulateddata now have their minor oscillations removed, and have meaningfulvalues at all pixels. Areas with no signal will have values near zero.Thus, it is possible to form a ratio of two components at the samepixel. At a pixel which previously would have been a trough, there isnow what amounts to an interpolated or fitted value which gives areasonable estimated value of a peak at the same location. At a pixelwhich previously would have only been a peak, there is likewise anavailable estimate of a trough. And in between, there are high-qualityfits to both peaks and troughs. Thus, the main source of error isremoved, which used to arrive from changes in tissue signal as one movedfrom a peak location to a trough location. This greatly improves thequality of the B1 map in areas where the MRI tissue characteristicschange.

On a pixel-by-pixel basis, the next step is to form a ratio of theminimal signal to the maximal signal. This ratio can be called the “tagdepth” where a value approaching zero indicates near complete darkening(saturation) by the total tagging RF angle. The total tagging RF angleis then determined by taking the inverse cosine (arccos) or cos⁻¹ of thetag depth TD=min/max. When the min is close to the max, TD is just lessthan one, and the tagging has minimal effect. When min is close to zero,then TD is also small which indicates the efficacy of the imposedtagging is close to 100% saturation.

Optionally, alternative measures might be generated for storage ordisplay. For example, a “tagging efficiency” defined as (1−min/max)might be favorable for ease of human comprehension, as a value near 1.0would then represent highly effective tagging saturation and 0.0 wouldbe completely ineffective tagging.

The B1 field can be saved in any of a few representations. It isreasonable to express the value at each pixel as the magnetic fieldstrength of the effective transmit RF field. Alternately, it isreasonable to show the flip angle of a particular pulse, or the totaltagging RF pulse.

Another favorable representation of the B1 map is to form a ratio,giving the actual local value normalized by the nominal value specifiedin the sequence. This ratio could be formed between tip angles, orbetween B1 field strengths, etc. In such a representation, a value over1.0 would indicate “over-tipping”; 1.0 is the ideal value, and valuesunder 1.0 indicate under-tipping. Such a representation can be usefulbecause it includes not just the spatial variation of the B1 Tx field,but it also captures any effects of calibration or system gain errors.It characterizes the entire MR system transmit RF, including possibledeviations in calibration, transmitter gain, etc.

Within reason, the time from the tagging to the excitation pulse shouldbe kept short, especially compared to the T1 values of the materials, tominimize a source of bias, where T1 relaxation of the tagged nucleicould cause their amplitude to be under-estimated, and the B1 value alsounderestimated. Similarly, the duration of each individual tagging pulseshould be kept short, as otherwise off-resonance during a pulse can leadto different effective tip angles. In particular, off-resonance canintroduce a bias, and underestimating of the RF pulse angle and the B1.

A typical data acquisition sequence is depicted at FIG. 2 where a SPAMMpre-sequence precedes a conventional MR imaging sequence. Here, in thisparticular example, two 30° RF nutation pulses are transmitted into theimaging volume and between them, a SPAMM magnetic gradient pulse isinterleaved. The spatial modulating frequency will be proportional tothe integral of the tagging gradient. An optional spoiler pulse may alsobe employed after the pre-sequence and before the conventional MRimaging sequence begins. As will be appreciated, the received RF signalsoccur later during the conventional MR imaging sequence. However, theywill have been spatially modulated because of the pre-sequence depictedat FIG. 2. In the example of FIG. 2, the SPAMM spatial encoding (i.e.,“tagging”) gradient pulse is imposed by using G_(y) (typically the phaseencoding gradient in a conventional MR imaging sequence), although itcould also be imposed via the G_(x) gradient (which is shown inparenthesis in FIG. 2). The optional spoiler pulse could be provided byany of G_(x), G_(y) or G_(z). Typically, G_(z) is used as the“slice-select” gradient during subsequent RF excitation pulses in aconventional MR imaging sequence, while G_(x) is applied during read-outof, for example, an RF echo response in the time domain so as tofrequency encode the read-out RF signals in the x spatial dimension.

A high level schematic depiction of an exemplary process is provided atFIG. 3. Here, at 300, k-space MR image data is acquired with cosine-likespatial modulation (e.g., at a spatial frequency k_(f) that isdetermined by the tagging gradient used during the pre-sequence as notedabove).

As earlier indicated, some advantages can be had by twicetwo-dimensionally Fourier transforming the originally acquired k-spacedata so as to create a processed “starting” k-space data set beforefrequency filtering operations are performed in accordance with thisembodiment.

As depicted on the right side of FIG. 3, one row of k-spaced data in thespatial domain will have superimposed modulation at a spatial frequencyk_(f).

The “starting” k-space data set is then frequency filtered at 310, 320and converted to the spatial domain (e.g., by 2DFT). The filter bank 310is a low-pass filter providing magnitude output L, while the filter bank320 is a high-passband filter with passbands located above and below thelow-pass filter bank at ±k_(f). The filtered higher passband spatialdomain data sets (e.g., based on harmonics of the base band signal) arethen demodulated at 330 (e.g., by taking absolute values of complexvalues) to provide a pair of higher frequency envelopes +E and −E. Roughschematic depictions of an exemplary one row of data across the image inthe spatial domain are depicted to the right in FIG. 3 for reach ofthese outputs.

At 340, a smoothed “upper” curve (L+E) is derived, while at 350, asmoothed “lower” curve (L-E) is derived. Once again, a depiction of onerow of data cross the image in the spatial domain is shown to the rightside of FIG. 3.

At 360, a “tagging depth” ratio R can be calculated at each pixel bytaking a ratio between the “lower” and “upper” data magnitude values.This ratio can then be converted at 370 to an effective nutation RFpulse angle θ (which is proportional to B1 magnetic field strength) byusing an inverse trigonometric function. For example, the quantity L/Ucan be used in conjunction with the arccos function so as to compute θ.Of course, as will be appreciated, θ can be converted to B1 magneticfield strength and either or both θ, B1 values can be normalized withrespect to the nominal expected control values used for the originalpre-pulse nutation modulation.

Finally, at 380, the resulting θ, B1 map data can be displayed, storedin machine-readable accessible storage media, or otherwise used (e.g.,by retrieving it from storage data) to compensate a diagnosticimage—perhaps for the very same patient anatomy that was in place duringthe derivation of the B1 map data.

A more detailed program code structure is depicted at FIG. 4 for the MRIsystem of FIG. 1. Here, if a B1 mapping process is chosen, the processis initiated at 400. Thereafter, at least one set of k-space data taggedwith spatial modulation is acquired at 402. For example, it may beacquired with a known spatial modulation frequency f_(m). Althoughvarious sizes of k-space data arrays may be used (e.g., 32×32, 64×64,128×128, etc.), for a hypothetical example, it may be assumed that f_(m)is equal to one cycle every 2 cm or 0.5 cm⁻¹. Let it also be assumedthat the k-space array is a 128×128 point array covering a square 256 mmslice of the imaging volume. This equates to an approximately 0.2 cm perpixel resolution, meaning that there are about five lines of spatialmodulation per centimeter, and a total distance of about 12.8 k-spacedata points between harmonics of the base band signal appearing at theorigin of k-space (i.e., k_(x)=0 and k_(y)=0 at the center of k-space).In this example, then a base band strip of k-space approximately twelvelines wide and centered upon the middle “zero” line would constitute thebaseline low frequency filtered portion of k-space. A similarly sizedstrip just above the baseline strip of about twelve lines wide wouldthen constitute the high-pass “positive” filtered segment of k-space,while a similar twelve line segment or strip located just below thebaseline across k-space would constitute the high-pass “negative”frequency filter passband.

As those in the art will appreciate, the variables could otherwise bechosen such that the entirety of k-space would simply be divided intothirds with the middle third being the base band low-pass frequencycomponent and the upper and lower thirds being the positive and negativehigh-pass filtered components, respectively. When k-space is evenlydivided in this manner, it facilitates the design of the transitionbands of the high-pass and low-pass filters, as will be appreciated bythose in the art.

If desired, at 404, a decision point may be inserted as to whether ornot one wishes to compensate for MRI system variables by performing afirst two-dimensional Fourier transform of the original k-space data at406 into the spatial domain and then a second two-dimensional Fouriertransforming from the spatial domain back to the frequency domain at 408before arriving at a suitable “starting” k-space data set. Of course, asthose in the art will appreciate, this may be done automatically all thetime or never rather than to provide a user-controlled decision point404.

The appropriate desired “starting” k-space data is then frequencyfiltered by dividing it into at least three portions (in this exemplaryembodiment): a low-pass baseline part=LP, a high-pass positive modulatedpart=HP+ and a high-pass negative modulated part=HP−.

Each of the frequency filters (e.g., extracted parts) of k-space dataare then two-dimensionally Fourier transformed so as to convert themback to the spatial domain—and demodulated by using only the magnitudeof the spatial domain values at 412, 414 and 416, respectively.

Thereafter, on a pixel-by-pixel basis, all three of the filteredsub-sets are summed at 418 to provide a map of peak or maximum signalenvelope values. At 420, a difference is taken between the low-passbaseline magnitude values and the sum of the high-pass side bands so asto provide a pixel-by-pixel map of the trough or minimum signal envelopevalues.

Thereafter, at 422, on a pixel-by-pixel basis, a tagged depth value iscalculated which, in this exemplary embodiment designed for useultimately with an arccos function, is calculated at min/max. As will beappreciated, at each pixel, this value then involves taking the ratio ofthe minimum to maximum values.

Thereafter, in this exemplary embodiment, at 424, the arccos of thetagged depth value is calculated for each pixel so as to derive aneffective RF flip pulse angle θ for each pixel, thus providing a map offlip angle θ values. If desired, the θ values may be converted to B1magnetic field strength values at 426 using well known formulae.

In addition, if desired, normalized θ and/or B1 map values can begenerated at 428. Any or all of such θ, B1 map values are then storedand/or displayed and/or printed at 430 as may be desired. Such mapvalues can also be used at 432 so as to compensate diagnostic imagesfrom the MRI system (perhaps from the very same patient that was used togenerate the B1 maps) and/or to design improvements to the MRI systemand the like, as will be appreciated by those in the art. Exit from thisroutine is taken at 434 and, as schematically depicted in FIG. 4, theprogram code structure may be configured with optional exits (or jumpsto a desired type of mapping) at many desired points (e.g., at 436, 438,440, 442 or 444).

Some enhancements (enumerated as 1-15E below) can provide optimizationsof the acquisition pulse sequence, as ways to enhance the overallperformance of B1 mapping. In narrow terms, the exemplary embodiment ismainly a processing and analysis process. But in broader terms, theoverall method can be improved in some cases, by coupling the processingwith an enhanced acquisition, and that acquisition enhancement may nothave special significance outside its use with the exemplary embodimentsdesired herein.

Enhancement 1: Higher harmonic terms may be used to fit more complicatedmodulations. This can extend the dynamic range of RF tagging pulseamplitudes, beyond the sinusoidal patterns associated with magnitudeimage reconstruction and tags of less than 90° RF amplitude. Differenttag line patterns are shown in the Bernstein, King and Zhou book. Forexample, to extend dynamic range of tagging pulses, one couldcharacterize the tagging shape, by showing how the first two, three orfour Fourier components of the modulation pattern are expected to varywith the total tag RF angle. Then, one can window and reconstructmultiple harmonics independently, and finally one can select the taggingangle which has the expected ratio of components which most closelymatch the data at a pixel.

Enhancement 2: The time shift between the component RF pulses insideSPAMM-like tagging pre-pulse can be constrained, so that the shift ofthe tag lines for the off-resonance difference between fat and water issubstantially a multiple of the time period needed for one cycle ofphase to accrue between these species. For example, at 3T, the taggingpre-pulse could be generated by two pulses, timed such that the delayfrom the center of one pulse to the center of the next pulse is about2.3 milliseconds. This time increment is known in other MRI pulsesequences as a “fat-water in-phase echo time.” The reason to do such isso that the location of stripes in fat and stripes in water signal arethe same, and fractional shifts of the RF tagging pattern are notencountered when crossing a fat-water interface. This makes thefiltering and separation of the modulated component more robust.

Enhancement 3: If an echo train-based readout technique [EPI, FSE, FASE]is applied after the tagging, the effects of amplitude decay modulationof the echo train must be considered. The effect of the amplitude decaymust be identical in each replicant. Otherwise, if different signalcomponents were centered at different parts of the amplitude decay, thenthe different replicants would have different T2 decay, and theiramplitudes could not be directly used in ratios, without error orbiases. Therefore, the shift direction of the replicants should occuralong the readout direction in k-space.

Enhancement 4: The filtering of the k-space data as described is alongone direction. The resultant B1 map will have its spatial resolutionlimited in that direction. However, in the opposite direction within theimage, higher spatial resolution may be obtained. Filtering can involvecollecting and merging in two directions—one of which achieves goodresolution near a horizontal edge direction, and the other of whichachieves good resolution near a vertical edge direction.

Enhancement 5: If two excitations are desired without waiting for fullrecovery, this might be done by collecting them with different spacingtag orientation shifted 90° (or tag spacing shifted). While the firstset of tags may not have fully recovered, that first set can be ignoredif it falls outside the window (in k-space) which would be needed tofilter and separate a second set of tags, and so on.

Enhancement 6A: Signed or complex image input may be utilized (i.e., notthe usual magnitude reconstruction of complex signal). Then, themodulation range can exceed a 90° total tagging angle, for betterdynamic range, while still using simple k-space filtering of the firstsinusoidal harmonic in the tagging pattern.

Enhancement 6B: When the spatial domain images used are magnitude orreal, as opposed to complex, then it is noted that the k-space datacontains Hermitian symmetry. It is possible to take direct advantage ofthe fact that shift frequency bands at positive and negative frequenciesare related by reflection about the center of k-space, and by complexconjugation. Thus, it is possible to perform alternate equivalentoperations such as windowing only the positive shifted frequency band,performing a 2DFT on it, and then generate the equivalent shiftedfrequency results by taking the real part of the 2DFT result andmultiplying it by 2. These variations derive from the basic mathematicalproperties of the Fourier transform, and are well known in the art.

Enhancement 6C: When the images used are complex, it is also possible towork with just one of the shifted frequency sidebands instead of boththe positive and negative direction shifted frequencies. As one example,it is possible to use one sideband, either the positive frequencyharmonic or the negative frequency harmonic, double its contribution,and not use the other shifted frequency sideband at all, while acceptingsome artifact or degradation in the resultant 2DFT spatial domainresults. It is also possible to use known MRI reconstruction techniquesfor reconstruction of partial datasets, in a way which reduces theartifacts. For example, a low resolution phase map can be generated fromthe main low-pass frequency image, and this phase map can be used forcorrection when synthesizing an equivalent 2DFT spatial domain imagecorresponding to what would result from the negative sideband. Thesekinds of methods are well known in the MR literature, where they arecommonly known as partial Fourier reconstructions, asymmetric k-spaceacquisitions, conjugate symmetry reconstructions, and the like.

Enhancement 7: At a major edge, such as the exterior of the body, therecan be point-spread issues which differ between the high-pass andlow-pass portions. This can lead to bad computed data for the flip angleor B1 in those areas. Similarly, this can occur near signal voids. Onestep in the processing can be to generate a mask to identify areas ofvery low signal, or very significant signal gradients, or both. Then anerosion operator may be used on the mask image, to remove edge regionsin the B1 map, which may have larger error.

Enhancement 8: Besides the map of B1, a secondary map such as p can begenerated, or a mask can be formed by thresholding of ρ, so that insubsequent operations using the B1 map, it is known for which pixels wehave generated a reasonable estimate of B1, and for which pixels thereis no such estimate available.

Enhancement 9: Relative amplitudes and/or relative phase of distinct RFtransmit channels could be determined by an extension of this method.Consider a system with two transmit coils. The acquisition pulsesequence could be repeated two or three times. In a first repetition, asingle transmit coil or channel could be used for both of the RF taggingpulses. In a second repetition, the two RF tagging pulses can be appliedwhere one coil is used to transmit the first pulse of the tagging pair,and the second coil is used to transmit the second RF pulse of thetagging pair, in which phase-sensitive maps of the modulation(high-pass) components can be generated from each map.

Optionally, a third repetition can be performed in which the second coilis used for both pulses. From the basic phase difference of the twomaps, one can compute the relative phase difference of the two transmitcoils. Many different similar alternatives should be easy to conceive byone skilled in the art, such as extension to larger numbers of coils.

Enhancement 10: Tagging structures other than two-pulse SPAMM can beused (however, the sinusoidal modulation that arises from two-pulseSPAMM does correspond to a particularly easy case for filtering ink-space, and for demodulating). In particular, any pattern that hasstructure which is locally substantially periodic should be a candidatefor filtering and separation in k-space.

Enhancement 11: The example diagram herein for processing shows theprocess beginning with magnitude images, then optionally performing areverse transform to convert back to a k-space data representation. Thiscan have certain practical advantages, such as implicitly allowing foruse of auxiliary functions that are performed in a productreconstruction (combination of data from multiple receiver coils beingone example). However, it is not necessary to convert to and from theimage domain before filtering. An alternative is to directly applywindow filtering and separation to the raw acquired k-space data,without first performing forward and backward transforms.

Enhancement 12A: Single-shot acquisition is a suitable choice for theimaging readout of this method (for example, single-shot EPI, orsingle-shot FSE, or as is available in Toshiba® MR application software,single-shot FASE). It is also reasonable, however, to use amultiple-shot imaging readout. If a multiple shot readout is used, thenthe preferred implementation is to allow the signal to recover from thetagging pulses, before re-applying the tag and collecting the next shot.For example, the recovery time could be in the range of three to fourtime constants of the typical range of T1 encountered in the tissues.This general advice would apply to any tagging analysis, and may not bespecific to the k-space filtered analysis.

Enhancement 12B: If more than one shot is needed, or more than oneimage, then one can contemplate using a saturation and spoiling pulsedirectly after each imaging readout. This would enable faster readout,i.e., maybe somewhat faster than TR=T1, without leaving residual bias tothe tag line intensities (the bias arising from unequal saturation andincomplete recovery). This general advice would apply to any tagginganalysis, and may not be specific to the k-space filtered analysis.

Enhancement 13: When extending the technique from 2-D maps, to 3-D maps,3DFT is a good choice if SNR is more limiting than motion. Alternately,sequential 2DFT acquisitions, separated by significant time for the tagsto recover between each slice, is a good choice of an imaging readoutsequence whenever control of patient motion is more critical than SNR.This general advice would apply to any tagging analysis, and may not bespecific to the k-space filtered analysis.

Enhancement 14: If windowing of the central lobe and shifted replicantsis done in one dimension, then increased energy from distant areas ofk-space may appear in the wrong window. This may lead to artifacts, suchas diagonal edges in the B1 map exhibiting a stair-stepping pattern orlocal superimposed “zebra stripes.” One simple way to reduce therelative error from signal being included in the wrong window is toapply a filter or window along the opposite direction in k-space. Theresult is a 2-D window or filter as depicted in FIG. 5.

Near the center of one replicant echo, for example, the power of thesignal from the modulated signal part will greatly exceed the power ofthe other two parts (unmodulated part, and other replicated part withwhose frequencies have the opposite sign). But at farther distances ink-space, the error signal from the other parts becomes comparable to, orpossibly even greater than, the power from the correct modulated part.Thus, these more distant areas contribute relatively more error, andshould have reduced weighting or should be completely windowed out ofthe individual processing of the individual components.

Another method to reduce error is simply to acquire fewer lines ofk-space.

As depicted in FIG. 5, the main unmodulated base band signal 500 appearsshifted to the left for a first “negative” harmonic at 502, and shiftedequally to the right at 504 for the first harmonic modulated “positive”signal in k-space. The diagonally extending hash marks from each of theprinciple lobes (depicted by circled crosses or plus signs) can thus beseen to extend into the center window region at 506 from the upper andlower side bands or harmonics. Accordingly, to help diminish thisunwanted effect, a 2-D window rather than complete strip of k-space canbe employed at 508 so as to filter out at least some of the interferingripples from adjacent side bands/harmonics. Similar 2-D windows (e.g.,rectangular, square, circular, etc.) can be utilized for all threecomponents of frequency filtering in k-space as depicted at 510 in FIG.5.

Enhancement 15A: The distant k-space signal from one signal component(i.e., from the unmodulated-component, or from themodulated-positive-frequency-component, or from themodulated-negative-frequency-component) can appear inside the mainfiltering window of another component (as also mentioned in enhancementor alternate embodiment 14). This signal can be thought of as a kind ofbaseline ripple, upon which the correct signal component is added. Ifthe baseline ripple can be reduced or removed, then the artifact will bereduced or removed. We now describe four technical ways to reduce orremove the “baseline” ripple.

Enhancement 15B: As depicted in FIG. 6, one can collect one taggedacquisition with the tags oriented in one direction (e.g., as in 602with the tagging gradient along the X direction for a transverselyoriented B1 map), and also collect a second tagged image, with the tagsoriented along the opposite in-plane direction as in 604, that is alongthe Y direction. With the two acquisitions in the two directions,replicants will occur with data at four locations, i.e., +kx, −kx, +kyand −ky. Select the scan parameters, including, for example, the k-spaceecho order and the phase encoding direction, so that as much as possiblewithin reason, the echo decay at the same locations in k-space is thesame. When the tagged components are shifted along the (plus-or-minus)kX direction, save a copy of the baseline ripple as detected by thewindows situated at the (plus or minus) ky-shifted locations at depictedat 606. When, in the other acquisition, the tagged components areshifted along the (plus-or-minus) kY direction, save a copy of thebaseline ripple as detected by the windows situated at the (plus orminus) kx-shifted locations. Subtract a copy of the measured baselineripple in each shifted window from the acquired modulated signal in thatsame window as shown at 610, 612, to at least partially reduce thebaseline ripple. Combine the maps from the two corrected acquisitions.

If the sequence uses an echo train-based readout technique (EPI, FSE,FASE, etc.), multiple shots of segmented k-space should be used. Here,the choice of phase encode schedule per shot is important. The phaseencode schedule dictates the amplitude decay modulation function. In thefirst acquisition (tag along X), by acquiring the readout directionalong the same direction of the shift (±kx), the central low frequencycomponent and outer high frequency components are centered within thesame position of the amplitude decay modulation function. All componentsexperience the same amplitude decay modulation. In the secondacquisition (tag along Y), the phase encode direction must be the sameas the first acquisition. Only the direction of the shift should change(to ±ky). The components must all be centered in the same positions ofthe phase encode schedule within each segment. The segment size, phaseencode schedule and/or tag cycle spacing must be chosen accordingly.Therefore, for the technique of baseline removal, if using an echo trainreadout method, the number of shots (segments) might naturally be amultiple of 3. A separate shot can be used for each component in thesecond acquisition to ensure that the component is centered in theamplitude decay function the same way. In this way, the ripple estimateregions of interest (A, B, C, D in FIG. 6) and the shifted componentsare all affected by the same amplitude decay modulation function in thesame way. Since the ripple estimate regions have the same amplitudedecay modulation as their corresponding shifted components, a directsubtraction can be performed.

Enhancement 15C: As in 15A, collect data with two (or more) orientationsof the tag data. Generate an uncorrected B1 map from each acquisition.Combine the images on a pixel-by pixel basis, such as by simpleaveraging, or by performing a weighted combination, with preferentialweighting at each location in image space for the B1 map which has theleast high-frequency content potentially interfering with the taggingmodulation patterns of each tagging orientation.

Enhancement 15D: Collect one copy of the acquisition with tags, and onewithout tags. Note the location where filter windows are placed over theshifted signal components with modulated signal in k-space. Fromcorresponding locations of windows over the untagged scanned k-spacedata, extract copies of the high frequency k-space data (these would bethe baseline ripples). Optionally, determine an amplitude factor,showing how the central untagged component of the data has reducedoverall amplitude in the k-space. Subtract the baseline ripple estimates(optionally multiplied by the factor for reduced amplitude). Proceedwith the rest of the map generation process.

Enhancement 15E: Collect two acquisitions, each of which could be usedto generate a B1 map. The first acquisition pre-pulse sequence shown inFIG. 7 a is as previously described for FIG. 2. However, in the secondacquisition at FIG. 7 b, the sequence is modified so that the spatiallocations of the peaks and troughs in the (sinusoidal) tagging patternare reversed. This may be done by inverting the polarity or phase of oneof the two RF tagging pulses. Suppose the first acquisition has atagging sequence which is symbolically denoted as (+αRF, Gtag_encode,+αRF). Then the second acquisition can have a sequence which issymbolically denoted as (+αRF, Gtag_encode, −αRF).

Extract the three components from each of the two acquisitions (asshown, respectively, at FIGS. 7 c and 7 d in which these six componentsare labelled as LP+alpha, LP−alpha, HP+alpha+freq, HP−alpha+freq,HP+alpha−freq, HP−alpha−freq where the part of the label either “+alpha”or “−alpha” refers to which RF polarity is used in the two acquisitions.Then, form some combinations by additions and subtractions:

LP=(LP+alpha)+(LP−alpha)

HP+freq=(HP+alpha+freq)−(HP−alpha+freq)

HP−freq=(HP+alpha−freq)−(HP−alpha−freq)

where LP is the low-pass (or unmodulated) component, and HP+freq andHP=freq are components which are modulated (high-pass) and shifted topositive and negative frequency displacements.

This phase cycling scheme causes cancellation of the baseline ripple.Other variants of phases will be obvious to those skilled in the art,i.e., they are corrected so as to have the contribution from theunwanted signal removed.

Proceed with the rest of the map generation process.

FIGS. 8, 9 and 10 are photographs of a particular implementation ofalternative 15E. Here, FIG. 8 shows the spatial domain image of a pelviswith the tagging lines shown. FIG. 9 is a normalized nutation angle θmap generated from the tagged image of FIG. 8. FIG. 10 shows the θ mapof FIG. 9 with superimposed contour lines where 1.0 means measured totaltip angle matches what was nominally specified, 0.80 means that the tipangles are 20% below that which was nominally specified, etc.

While only a few exemplary embodiments have been described in detailabove, those skilled in the art will recognize many novel features andadvantages of these embodiments may be realized even though many of thedetails are altered from the exemplary embodiments. All suchmodifications and variations are intended to be included within thescope of the appended claims.

1. A method for generating a B1 map in an MRI system, said methodcomprising using an MRI system to: (a) acquire at least one set of B1amplitude tagged MRI data signals in spatial frequency domain k-spacefrom MR nuclei within an imaged volume of the MRI system; (b) processsaid k-space data to produce at least two sub-sets of frequency-filteredk-space data: (i) a baseline low-frequency sub-set, and (ii) at leastone of a positive higher frequency sub-set including a harmonic versionof said baseline sub-set and a negative higher frequency sub-setincluding a harmonic version of said baseline sub-set; (c) separatelytransform each of said sub-sets to respectively corresponding spatialdomain data sets: (i) a baseline magnitude set, and (ii) at least one ofa positive harmonic magnitude set and a negative harmonic magnitude set;(d) arithmetically combine said baseline magnitude set with said atleast one of the harmonic magnitude sets on a pixel-by-pixel basis toprovide upper and lower magnitude data sets; (e) process said upper andlower magnitude data set values on a pixel-by-pixel basis to generate aB1 map value based on value related to a ratio of said upper and lowerpixel data values at a given pixel location in the spatial domain; and(f) store said B1 map of values in a computer accessible and readablememory device for subsequent use by said MRI system.
 2. The method ofclaim 1, wherein step (a) comprises: applying at least two RF excitationpulses with at least one interleaved magnetic gradient pulsepre-sequence before applying an MR imaging pulse sequence to elicitsuccessive NMR responses in the time domain which are mapped torespectively corresponding portions of a two-dimensional set of k-spacedata in a spatial frequency domain.
 3. The method of claim 2, whereinstep (a) further comprises: applying a 2DFT (two-dimensional Fouriertransform) to an originally-acquired set of two-dimensional k-space datato provide a two-dimensional set of spatial domain data; and applying a2DFT to said two-dimensional set of spatial domain data to provideanother two-dimensional set of k-space spatial frequency domain data foruse in subsequent step (b).
 4. The method of claim 2, wherein saidpre-sequence is a SPAMM (spatial modulation of magnetization) sequenceand step (e) uses an inverse cosine function of said ratio to generateB1 map values.
 5. The method of claim 2, wherein said pre-sequence is aDANTE (delays alternating with nutations for tailored excitation)sequence.
 6. The method of claim 1, wherein step (a) comprises:acquiring a first set of k-space data using a first tagging pre-sequenceof at least two RF excitation pulses having a same nutation angle sense;acquiring a second set of k-space data using a second tagging sequenceof at least two RF excitation pulses having different alternatingnutation angle senses; and arithmetically combining said first andsecond sets of k-space data on a pixel-by-pixel basis to produce acombined set of k-space data to be used in subsequent steps.
 7. Themethod of claim 6, wherein step (a) further comprises: applying a 2DFT(two-dimensional Fourier transform) to said combined set oftwo-dimensional k-space data to provide a further two-dimensional set ofspatial domain data; and applying a 2DFT to said further two-dimensionalset of spatial domain data to provide yet another two-dimensional set ofk-space spatial frequency domain data for use in subsequent step (b). 8.The method of claim 1, wherein step (b) comprises: extracting k-spacedata from a mid-portion of k-space to produce said baselinelow-frequency sub-set; extracting k-space data from a different portionof k-space disposed to one side of said mid-portion to produce saidpositive higher frequency sub-set; and extracting k-space data fromanother different portion of k-space disposed to another side of saidmid-portion to produce said negative higher frequency sub-set.
 9. Themethod of claim 8, wherein said extracting steps multiply respectivelycorresponding shaped window functions by k-space data.
 10. The method ofclaim 8, wherein said extracting steps extract horizontal or verticalstrips across k-space data.
 11. The method of claim 8, wherein saidextracting steps extract rectangular or square areas within k-spacedata.
 12. The method of claim 1, wherein step (c) comprises: separatelyapplying a 2DFT to each of said sub-sets of frequency-filtered k-spacedata to convert such into the spatial domain and then using only themagnitude value for each resulting pixel data point to respectivelyprovide said magnitude sets of spatial domain data.
 13. The method ofclaim 1, wherein step (d) comprises: adding all three magnitude sets ofspatial domain data on a pixel-by-pixel basis to provide a map of peakor upper signal magnitude envelope data set; and subtracting from thebaseline magnitude set the sum of the harmonic magnitude sets on apixel-by-pixel basis to provide a map of trough or lower signalmagnitude envelope data set.
 14. The method of claim 1, wherein step (e)comprises: creating a tag depth ratio (TD) data set on a pixel-by-pixelbasis where each pixel of the tag depth ratio data set corresponds toTD=min/max where min is the lower magnitude data set value and max isthe upper magnitude data set value; and calculating the arccos of TD ona pixel-by-pixel basis to provide a B1 map of effective tag nutationflip angles.
 15. The method of claim 14, wherein step (e) furthercomprises: calculating a normalized value for effective/intended tagnutation flip angles on a pixel-by-pixel basis to provide a B1 map ofnormalized tag nutation flip angles.
 16. The method of claim 14, whereinstep (e) further comprises: calculating B1 strength based on said tagnutation flip angles on a pixel-by-pixel basis to provide a B1 map ofeffective B1 field strengths.
 17. The method of claim 16, wherein step(e) further comprises: calculating a normalized value foreffective/intended B1 field strength on a pixel-by-pixel basis toprovide a B1 map of normalized B1 field strengths.
 18. The method ofclaim 1, further comprising: (g) displaying, on a display screen orprinter, said B1 map of data values for visual observation by a user ofthe MRI system.
 19. The method of claim 1, further comprising: (g) usingsaid stored B1 map of data values to provide image compensation to adiagnostic image acquired by said MRI system, thereby providing acorrected diagnostic image of improved quality.
 20. The method of claim1, wherein step (b) processes said k-space data to produce more thanthree sub-sets of frequency filtered k-space data by including furthersub-sets encompassing respectively associated higher harmonic componentsof the spatial modulation.
 21. The method of claim 20, whereindetermination of a B1 map value at each pixel includes a data fittingprocess using the associated higher harmonic components.
 22. The methodof claim 1, wherein step (a) comprises constraining the time shiftbetween pre-sequence tagging RF pulses so that the shift of the taglines for off-resonance difference between fat and water species nucleiis substantially a multiple of the time period needed for one cycle ofphase to accrue between these species.
 23. The method of claim 1,wherein step (a) utilizes plural RF transmit channels and an acquisitionpulse sequence is repeated plural times using different ones orcombinations of the RF transmit channels for respectively correspondingdifferent acquisition pulse sequences.
 24. A computer-readable storagemedium containing computer program code which, when executed, effectsthe method of claim
 1. 25. An MRI system comprising: (a) an MRI scannerconfigured to acquire at least one set of B1 amplitude tagged MRI datasignals in spatial frequency domain k-space from MR nuclei within animaged volume of the MRI system; at least one processor configured to:(b) process said k-space data to produce at least two sub-sets offrequency-filtered k-space data: (i) a baseline low-frequency sub-set,and (ii) at least one of a positive higher frequency sub-set including aharmonic version of said baseline sub-set and a negative higherfrequency sub-set including a harmonic version of said baseline sub-set;separately transform each of said sub-sets to respectively correspondingspatial domain data sets: (i) a baseline magnitude set, and (ii) atleast one of a positive harmonic magnitude set and a negative harmonicmagnitude set; arithmetically combine said baseline magnitude set withsaid at least one of the harmonic magnitude sets on a pixel-by-pixelbasis to provide upper and lower magnitude data sets; process said upperand lower magnitude data set values on a pixel-by-pixel basis togenerate a B1 map value based on a value related to a ratio of saidupper and lower pixel data values at a given pixel location in thespatial domain; and (c) a data memory configured to store said B1 map ofvalues in a computer accessible and readable memory device forsubsequent use by said MRI system.